Number of UFU-free Motzkin paths of length n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =47a(7) =112a(8) =274a(9) =679a(10) =1708a(11) =4341a(12) =11143a(13) =28831a(14) =75135a(15) =197013a(16) =519447a(17) =1376256a(18) =3662327a(19) =9784106a(20) =26232033a(21) =70558313a(22) =190348160a(23) =514904151a(24) =1396328313a(25) =3795324358a(26) =10338000693a(27) =28215285901a(28) =77149545999a(29) =211314835549